The generator matrix

 1  0  1  1  1 3X+2  1  1  0  1 3X+2  1  1  1  1 2X  1 3X  1  1  0  1  1 3X  1  1  1 X+2  1  2  1  1  1  2  1  1 3X+2  1  1  X  1  1  1  1 X+2  1  1  2 2X  2  1  0 2X+2 3X+2  1  1  1  1 2X+2  2 3X  1 2X 2X  X  1  1  X X+2  1 2X  1  1  1
 0  1 X+1 3X+2  3  1 2X+3  0  1 3X+2  1 X+1 2X+1 X+3 2X  1 3X  1 3X+3  0  1  1 3X  1 3X+3 2X+3  2  1 X+2  1 X+1 3X+2  3  1 3X+3  2  1  X  1  1  2 X+1  1 2X+2  1  3  3  1  1  X X+3  X  1  1 3X+1 X+1  3  3  X  1  1  X  1  1  1 X+2 3X+3  1  1 3X+2  1  2 2X+2 2X
 0  0  2  0  0  0  0  2 2X+2 2X+2  2 2X+2 2X  2 2X+2  2 2X 2X  2 2X 2X 2X  2 2X+2 2X+2  2  0  2  2 2X  0  0 2X+2 2X+2  0 2X+2 2X 2X  2  0 2X 2X  2  2  2 2X+2 2X  0  2  0 2X 2X+2  2  0  0  0 2X+2  2  2 2X+2 2X+2  2  0 2X  2 2X 2X+2 2X  2 2X+2  0 2X 2X 2X+2
 0  0  0 2X+2 2X 2X+2  2  2 2X+2 2X  0 2X+2  0 2X  0 2X 2X 2X 2X+2 2X+2 2X+2  2  2 2X+2  2  0 2X+2 2X+2 2X+2  2 2X  0 2X+2 2X  2 2X 2X 2X+2 2X  2 2X  0 2X+2  2  2  2  2  0  0 2X+2  2  0  2 2X 2X+2  0 2X 2X 2X+2  0  0 2X  2 2X 2X+2  0 2X 2X+2 2X 2X+2 2X  2  0 2X

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+68x^69+338x^70+500x^71+555x^72+382x^73+585x^74+344x^75+495x^76+374x^77+273x^78+80x^79+34x^80+36x^81+16x^82+2x^83+2x^85+2x^88+2x^89+3x^90+2x^91+1x^94+1x^100

The gray image is a code over GF(2) with n=592, k=12 and d=276.
This code was found by Heurico 1.16 in 0.531 seconds.